Based on the first-principles computational method and the elastic scattering Green's function theory, we have investigated the electronic transport properties of different oligothiophene molecular junctions theoretically. The numerical results show that the difference of geometric symmetries of the oligothiophene molecules leads to the difference of the contact configurations between the molecule and the electrodes, which results in the difference of the coupling parameters between the molecules and electrodes as well as the delocalization properties of the molecular orbitals. Hence, the series of oligothiophene molecular junctions display unusual conductive properties on the length dependence.